\[ % misc \newcommand{\~}{\widetilde} \newcommand{\<}{\left\langle} \newcommand{\>}{\right\rangle} \newcommand{\lc}{\lceil} \newcommand{\rc}{\rceil} \newcommand{\lf}{\lfloor} \newcommand{\rf}{\rfloor} \newcommand{\xla}{\xleftarrow} \newcommand{\xra}{\xrightarrow} % single letters \newcommand{\A}{\mathbf A} \newcommand{\C}{\mathbf C} \newcommand{\F}{\mathbf F} \newcommand{\G}{\mathbf G} \newcommand{\N}{\mathbf N} \newcommand{\O}{\mathcal O} \newcommand{\P}{\mathcal P} \newcommand{\Q}{\mathbf Q} \newcommand{\R}{\mathbf R} \newcommand{\S}{\mathbf S} \newcommand{\T}{\mathbf T} \newcommand{\U}{\mathrm U} \newcommand{\W}{\mathbf W} \newcommand{\Z}{\mathbf Z} \newenvironment{bmatrix*}{\left[\begin{array}{rr}}{\end{array}\right]} % spaces \newcommand{\I}{I} \Annotate[text]{\I}{unit interval $[0, 1]$} \newcommand{\Sone}{S^1} \Annotate[text]{\Sone}{unit circle in $\R^2$} \newcommand{\Dtwo}{D^2} \Annotate[text]{\Dtwo}{unit disk in $\R^2$} \newcommand{\Stwo}{S^2} \Annotate[text]{\Stwo}{unit sphere in $\R^3$} % algebra \DeclareMathOperator{\K}{K} \DeclareMathOperator{\End}{End} \DeclareMathOperator{\Hom}{Hom} \DeclareMathOperator{\Ext}{Ext} \DeclareMathOperator{\Tor}{Tor} %\DeclareMathOperator{\ker}{ker} \renewcommand{\im}{\mathrm{im}} \Annotate[text]{\im}{Image} \DeclareMathOperator{\coker}{coker} \DeclareMathOperator{\Spec}{Spec} \DeclareMathOperator{\Spf}{Spf} \DeclareMathOperator{\Aut}{Aut} \DeclareMathOperator{\Gal}{Gal} \DeclareMathOperator{\GL}{GL} \DeclareMathOperator{\SL}{SL} \DeclareMathOperator{\SO}{SO} \DeclareMathOperator{\gr}{gr} \newcommand{\Defeq}{\mathrel{:=}} \newcommand{\psr}[1]{[\![#1]\!]} \newcommand{\tnsr}{\otimes} \newcommand{\Fil}{\mathsf{F}} % THH \DeclareMathOperator{\THH}{THH} \DeclareMathOperator{\TC}{TC} \newcommand{\TCmin}{\TC^-} \DeclareMathOperator{\TF}{TF} \DeclareMathOperator{\TP}{TP} \DeclareMathOperator{\TR}{TR} \DeclareMathOperator{\TS}{TS} % prismatic \newcommand{\Nyg}{\mathcal N} \newcommand{\prism}{ \class{prism}{\Delta} } \newcommand{\syn}{\mathrm{syn}} % equivariant \newcommand{\rog}{\bigstar} \DeclareMathOperator{\RO}{RO} \newcommand{\regconn}[1]{\mathop{\mathsf{P}_{#1}}} \newcommand{\regslice}[1]{\mathop{\mathsf{P}^{#1}_{#1}}} \newcommand{\m}{\underline} \newcommand{\mpi}{\m\pi} % spaces \newcommand{\RP}{\mathbf{RP}} \newcommand{\CP}{\mathbf{CP}} % coding \newcommand{\r}[1]{\mathrm{#1}} \newcommand{\qeq}{\mathrel{\text{“=”}}} \newcommand{\red}{\textcolor{var(--red-9)}} \newcommand{\green}{\textcolor{var(--green-10)}} \newcommand{\blue}{\textcolor{var(--blue-11)}} \]

Math

I am no longer in academia. Previously, I was a Tamarkin Assistant Professor of Mathematics at Brown University, working with Tom Goodwillie. I received my PhD from the University of Texas at Austin under the supervision of Andrew Blumberg.

I am interested in algebraic K-theory, particularly trace methods; equivariant stable homotopy theory; higher category theory; and Goodwillie calculus. I am also frequently interested in how these interact with arithmetic geometry, particularly crystalline/prismatic cohomology.

I have compiled a reading list for \(p\)-adic cohomology and its connections with THH.

Publications / Preprints

Prisms and Tambara functors I: Twisted powers, transversality, and the perfect sandwich. Preprint, 2023.
\(\mathrm{RO}(\mathbb T)\)-graded \(\mathrm{TF}\) of perfectoid rings. Preprint, 2022.
Floor, ceiling, slopes, and \(K\)-theory. Annals of $K$-Theory 8 (2023), no. 3, 331–354.
- arXiv version
- Interactive figures
A slice refinement of Bökstedt periodicity. Preprint, 2020.
\(\infty\)-categorical monadicity and descent. New York Journal of Mathematics 23 (2017), 749–777. arxiv version.

Visualizations / Tools

I make videos about math at Epiplexis. Here are some additional math interactives I have created.